Weighting of charge in PIC codes for unstructured meshes in cylindrical coordinates: application to charged jets

Some problems arise in particle-in-cell (PIC) codes when computing the density of charge at the nodes in cylindrical coordinates, especially near the axis. Several authors has different ways to correct these problems for structured meshes in finite-differences calculations. Here we propose a general method to lessen this problem in unstructured meshes both triangular and quadrilateral, following the work by Verboncoeur for structured meshes. This technique also improves the charge assignment in cartesian coordinates.